As always, Mathsconf never disappoints. Yet another brilliant day of CPD delivered by people who are in the classroom day in, day out and so understand the pressures of teachers and the reality of their workload.

As always, there is the cake competition with lots of mathematical themed cake.

The tower of doughnuts certainly were great to look at and very tasty too.

In the introductory session we were told about LaSalle’s big announcement:

Autograph is free for everyone, forever! We were treated to a very quick demonstration by the creator of autograph. I must say, I didn’t realise autograph could actually do so much. It will certainly be worth some time playing around with.

**Session 1 **

This time I decided to take the plunge and deliver a session myself. I started teaching A-Level maths 3 years ago, the same time I took on my first role as head of department. Talk about hitting the ground running. With the help of members of my departments, some brilliant courses and excellent resources, I now feel confident standing in front of year 12 and delivering the content. This was not always the case however. For the whole of the first year I was nervous every time I entered that classroom, I was worried about what the students would ask and I just felt like a bit of a fraud. I wanted to share the resources that had really helped me and let any teacher know who is starting out in A-Level that it is normal to feel the way I did.

If you would like to see a copy of my slides they are here:

**Session 2 – Making the most of examples** @BerwickMaths

This session did exactly what the name suggested, it looked at examples we use in the classroom and how to get the most out of them.

Joe was taking inspiration from Craig Barton’s book, How i wish i taught Maths.

Below is something I already use myself quite a lot and certainly am pleased with how the students have responded to this.

Joe made a brilliant point and said that this is great for short examples with maybe one or two steps but one you start getting into processes that are longer and more complex, students may need some extra support and guidance.

Enter, the supercharged example:

The idea here is that you start with the worked example, you then get the students to reflect upon what they have just done, you then do an example by fading (this is where the teacher starts the example and stops at a point during the example and make the students complete it) and finally your turn where the students complete the whole example on their own.

I really liked this idea and have already implemented this into my lessons where appropriate. I used it with my year 7s this when when finding the surface area of a cuboid. I made a slight adjustment with the reflection. I started the sentence and then asked the students to complete the sentence.

These examples would then be followed up with practise (the questions below are an example of practise and do not follow on from the examples above):

Joe then went out to talk about covertization;

Joe used the example of simultaneous equations and getting students to decide if you could use elimination. He simply changed the coefficients of the variables around and changed the subject a few times but ultimately the numbers were the same.

I certainly need to do some more research into this as a method and try and understand the concept more before I try implementing it myself.

Overall, I certainly gained something from this session and Joe has very generously created a free website with his supercharged examples on. Follow him on twitter to find out more.

**Session 3 – A trip down memory lane: getting the students to remember **@mrcollinsmaths

This session looked at memory and trying to encourage students to remember the things we have taught them. I am sure we all know this is currently a very hot topic and one in which is being discussed in education right now.

Paul went through 10 different areas which he has come across to help with memory but looked specifically at daily review and weekly/monthly review.

One of his first suggestions is to use last lesson, last week, last term in lessons a starters or plenaries:

This is something that I have used quite a lot in lessons with many different year groups. Jo Morgan shared some ideas on it previously and so i decided to implement into my lessons. I have shared this idea with my department and know that several of them have also adopted this as a method. As Paul said, this starter doesn’t have to take long to create. Simply snip appropriate questions from good websites and pop them into the template.

Paul also then shared another idea that he uses for starters:

Again the focus is on knowledge gained in a previous knowledge but key information has been blocked out. This method may help students as I view this as more of a prompt for students. This is certainly a method I want to try out and see how students respond. I think my year 11 set 5 would like this as they would have something to help jog their memory but at the same time it is making them use their own recall.

Paul recommend some books that are worth reading:

I am in the process of reading Craig Barton’s book but need to put making every maths lesson count by Emma McCrea onto my reading list.

**Session 4 – Teaching the why before the how @mrmattock**

I have been following Peter on twitter now for a few years and love the things that he shares. I am a massive fan of his goal free problems and have used these in lessons on several occasions. When I saw that Peter was delivering a session at mathsconf I certainly wanted to go along.

Peter made such a good point, we use various different images to represent the same concept. Take factorising for example, it ranges from factor trees, to grids being drawn to brackets. We as teachers know that all of these things all reference factorising but do the students? Is it better if we try and show one image for one concept?

Peter started off with the task above. Using only the rods in the picture create rectangles with areas of 8, 12, 9 and 13.

Straight away this should be accessible to all students. They should know how to find the area of a rectangle and should be able to do this. We also know as teachers that they have actually just found the factors of the numbers. I heard someone near me comment, what a great way to get students thinking about factor pairs.

From there we took 18 as an area and drew the appropriate rectangles. Peter then said that using only rods of prime numbers could we make the sides. So for example, a 6 x 3 rectangle can be made from 3 lots of 2 rods and 1 lot of 3 rod which is 3 x 2 x 3 which is the prime factorisation of 18. Or you could have 2 lot of 3 rods and a 3 rod which is again 2 x 3 x 3. Or a 9 by 2 rectangle can be made from 3 lots of 3 rods and a 2 rod which is 3 x 3 x 2.

We then started looking at algebraic examples and using a rod of length ‘x’ and 1 by 1 rods and factorising expressions such as 2x + 2. So we had to draw out 2x + 2 rectangle and then place the appropriate rods around the side.

After a few of these we moved onto more complex factorisation involving square terms:

Peter did acknowledge that some teachers may not want to represent -1 or -x as an area and so you could build the students up with the positives and then when they can build from the concrete to the abstract introduce negative areas. As Peter said eventually most models break down but we try and get the students the abstract through the use of concrete.

Mathsbot is the website that we were using for the rods so I would recommend going on there and having a play around with this idea.

**Session 5 – A rummage through the archives** @aqamaths

Its always great to be welcomed into a session with some warm up questions to complete. As you can see, calculators have not been invented yet when these questions were published. I would love to know how students would cope with these today (have to admit, I couldn’t access Q3 due to being born after decimalisation).

This session was an interesting one, in many ways it shows how we are sort of heading back to the question style of O-Level maths. Don’t get me wrong, the way in which the qualification is offered is different but as Andrew commented a few times, change the wording a little bit and it wouldn’t be out of place on a paper today.

We played our usual game of ‘guess the year’, I scored an abysmal 0%:

Andrew showed us the attainment in 1979 (notice how only 77.1% of students were entered into exams):

We then looked at how GCSE has changed in terms of the percentage of content that is now examined since the reforms:

So both number and ratio/proportion and increased, stats and geometry has decreased and algebra has remained steadfast.

We then looked at the old structure of the O-Level exams:

Notice how there was a choice in question in section B which were all 15 marks each. However, these questions were rather structured:

I think that our higher end students would actually find this question very accessible and would be thankful for the breakdown throughout the question.

Compare this question to the exam style of the current GCSE and I think the question would be less structured and more geared towards problem solving.

Andrew finished by showing us one of his favourite questions:

Anyone with a very able year 11 group, why not set them this as a challenge?

Once again, Mathsconf21 delivered a brilliant day of CPD and networking. If you haven’t attended one yet then make sure you get to the next one!